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COPYRIGHT DEPOSIT. 



Mechanical Drawing 



BY 



OSWALD GUETH, m. e., ll. b., 

Jl . 

Professor of Mechanical Drawing and Machine Design 

Cooper Union Schools of Science 
NEW YORK 




THEO. AUDEL & COMPANY 

PUBLISHERS 
72 FIFTH AVENUE. 



NEW YORK 



T 3 SI) 



Copyright, 1913, 

BY 

OSWALD GUETH. 



ir fO^ 
■CI.A354599 



PREFACE 



This book is the result of years of experience in the drafting room 
and behind the desk. The methods pursued therein combine the best 
practice in this country and abroad, based on the writer's intimate 
knowledge of German engineering education. 

While the book is primarily written for Engineering Colleges, with 
certain omissions, it furnishes an excellent textbook for High Schools, 
Trade Schools, Evening Drawing Classes and Home Study. 

The course to be covered by the Cooper Union Schools is with slight 
modifications roughly as follows : 

Day School of Technical Science: 

1. Year of drawing: Chap. I. to V. incl. 

2. Year of drawing: Chap. VI. (in conjunction with Text- 

books on Elementary Design.) 

Evening Schools of General Science and Electrical Engineering: 

1. Year of drawing: Chap. I. to HI. B. incl. 

2. Year of drawing : Chap. HI. C. to VI. A. incl. 

The Chapters IV. and V. are curtailed to some extent in the Evening 

Schools. 

The merit claimed for this work is the systematically-arranged selec- 
tion of lessons in form of drawing plates which, for the greater part, are 
reproductions as to size of f)aper and proper arrangement of the problems 
of the finished drawing. 

The problems, of course, are unfinished on the printed plate, and 
their specifications, given in the text, may vastly vary with every in- 
structor, but the underlying principles of construction in each case are 
expressed "graphically" ; that is, in the language of the Draftsm.an. And 
thereby the author has tried to avoid the great evil, of which most other 
books on iMechanical Drawing suffer, namely : big books with a whole 
lot of reading matter (zvhich is hardly ever read by the student) and very 
little (usually poor) drawing. 

The explanations in this book are simple and direct, stripped of all 
needless words, teaching the student to develop his own thinking power. 



CONTENTS 



Chapter I. Introductory Remarks. page. 

A. Drawing Tools and Their Use 1 

B. Drafting Room and Shop Practice 2 

C Laying Out Sheet and Lettering 3 

D. Important Rules As to Working Drawings 7 

Chapter II. Simple Working Drawings. 

A. Three Views and Isometric 12 

B. Simple Models 15 

C. Wooden Joints and Carpenter Work 21 

D. Machine Drawings 21 

Chapter III. Projection Drawing. 

A. Proj ections 32 

B. Sections 37 

C. Intersections 53 

D. Warped Surfaces 65 

Chapter IV. Perspective Drawing. 

A. Method of Plan and Elevation 69 

B. Method of Two Vanishing Points 75 

C. Method of One Vanishing Point 78 

Chapter V. Shades and Shadows. 

A. Points, Lines and Planes 81 

B. Prisms and Pyramids 85 

C Spheres 89 

D. Screw Surfaces 91 

E. Shadow Perspective 91 

Chapter VI. Advanced Mechanical Drawing. 

A. Working Drav/ings 97 

(a) Globe Valve. 

(b) Steam Engine. 

(c) Electric Generator. 

B. Elementary Designing and Construction ' 101 

(a) Riveted Joints and Structural Work. 

(b) Cams. 

(c) Tooth Gearing. 

(d) Valve Motion Diagram. 



LIST OF PLATES. 

(All plates to be rendered in ink on paper or tracing cloth as specified 

by Instructor, except plates 1 to 10, which may all or partly 

be done in pencil on detail paper.) 

Plate. Simple Working Draz^^nngs. 

1. Wooden Models. 

2. Metal Models. 

3. Machine Details. 

4. Wooden Joints. 

5. Frame Work. 

6. Drawing Table. 

7. Bolts and Xuts. 

8. Pillow Block. 

9. Shaft Coupling. 

10. Pipe \\"ork. 

Projection Drazi'ing. 

11. Projections of Prisms. 

12. Projections of Pyramids. 

13. Inclined Prisms. 

14. Inclined Pyramids. 

15. Sections of Prisms and Pyramids. 

16. Conic Sections I. 

17. Conic Sections II. 

18. Spheric Sections. 

19. Sections of Various Solids. 

20. Intersections of Prisms I. 

21. Intersections of Prisms II. 

22. Intersections of Cylinders I (Steam Boiler). 

23. Intersections of Cylinders II. 

24. Intersections of Spheres. 

25. Intersections of Prisms with Pyramids. - 

26. Intersection of Cone with Oblique Prism. 

27. Intersection of Cone with Pyramid. 

28. Warped Surfaces. 

Perspective Draining. 

29. Perspective by 1. ^vlethod. 

30. Perspective by 2. ^lethod. 

Shades and Shadows. 

31. Points. Lines and Planes. 

32. Prisms and Pyramids. 

33. Sphere and Ellipsoid. 

34. Screw Surfaces. 

35. Shadow Perspective I. 

36. Shadow Perspective II. 

Advanced Mechanical Draining. 

37. Globe Valve. 

38. Marine Engine. 

39. Electric Generator. 
40. 

41. 

42. Rivets and Riveted Joints. 

43. Steam Boiler. 

44. Roof Truss. 

45. Cams I. 

46. Cams II. 

47. Curves for Tooth Construction. 

48. Tooth Gearing I. 

49. Tooth Gearing II. 

50. Valve Motion Diagram. 








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MECHANICAL DRAWING. 



CHAPTER I. 
INTRODUCTORY REMARKS. 

A — Drawing Tools and Their Use. 

"A good draftsman must have good instruments" goes with- 
out saying. That is, the best instruments obtainable are just good 
enough. They need, however, not be elaborate, and, perhaps, for 
young beginners, may be of a cheaper quality, until the student 
has found out whether he is gifted for the art of drafting. 

The following is a list of all that is needed to begin drawing : 

1 set of instruments. 1 bottle of black drawing ink. 

1 drawing board. 2 pencils, 3H and 6H. 

1 tee-square. 4 thumb tacks. 

2 triangles, 30° and 45°. 1 ink and pencil eraser. 
1 scale (for different scales use tri- 1 penholder with pen. 

angular boxwood scale). 

Later on he may need one French curve for drawing such 
curves that cannot be drawn with the compass, one protractor, to 
measure various angles, one pair of calipers, to take measure- 
ments from models when sketching. 

Instruments. — They should at the least contain the follow- 
ing 4 parts : 

1 compass, for drawing circles and arcs with pencil or ink. 
1 pair of dividers, for dividing lines into certain required 
parts or transferring dimensions from one part of the 
drawing to another. 
1 riding pen for drawing straight lines. 
1 bow pen for drawing very small circles and arcs. 



2 MECHANICAL DRAWING. 

Tee-Square and Triangles. — By means of the Tee-square, 
which rests with the head against the left edge of the board, all 
horizontal lines are drawn along the upper edge of the blade. By 
means of the Triangles all vertical lines are drawn (draftsman 
turned to left and drawing the lines upward). By combining the 
triangles as shown in Fig. 1, various other angles may be drawn. 
(Draftsman should try to obtain such angles by different positions 
of triangles.) 

B — Drafting Room and Shop Practice. 

Drafting Room. — The personnel of a modern drafting room 
usually consists of a chief draftsman and a number of design- 
ers or draftsmen having an engineering knowledge. Each 
designer has a number of assistants, to make tracings and 
detail drawings. There will also be one or more persons to 
make blue prints, take care of the drawings and probably act 
as time keeper. 

Working drawings are generally made on brown detail 
paper in pencil, traced on tracing cloth and then blue printed. 
The process of tracing is as follows : Place the tracing cloth 
over the pencil-drawing, either side of the tracing cloth being 
used for inking in. Then rub powdered chalk with a soft rag 
on it, in order to make the cloth take the ink well. The 
powder must be rubbed off gently. Before attempting to draw 
any lines on the tracing cloth, try the pen on the edge of the cloth 
outside the boundary lines on which the tracing is to be cut, until 
the pen works freely and produces lines of the required thickness. 

Machine Shop. — The blue print is first sent to the pattern 
maker, who makes a model in wood from it (if it is to be a 
casting). From his experience he makes proper allowance 
for ''shrinkage" of the casting during cooling, for ''finishing" 
and for a certain amount of taper for "draft" in withdrawing 
the pattern from the mold. 



INTRODUCTORY REMARKS. 3 

The pattern is then sent to the foundry to be molded in 
sand. The form is filled with melted ore from the cupola. 
After the casting has cooled off, it is sent to the machine shop 
to be drilled, tapped, finished or whatever the drawing calls 
for, for the machinist must strictly follow all instructions, 
dimensions and notes contained in the drawing, thereby plac- 
ing all the responsibility of error upon the draftsman. 

This same strict rule applies to all working drawings, 
whether used in the machine, structural, woodworking or 
building trade. 

Sketching. — When making drawings of a machine it would 
be inconvenient to carry board and instrument into the shop. 
The draftsman therefore is called on to make "sketches," carry 
them to the drafting room and make his drawings from them. 

Each piece of the machine should be sketched separately 
and a complete working drawing made of it. After each piece 
has been sketched, make a rough general sketch of the whole 
machine, to show how the various pieces fit together, a few of 
the most important over-all dimensions, distances between 
centers, etc. 

Before starting to sketch a piece, decide what views are 
necessary to describe the piece clearly. Make large sketches. 

The sketches should be neat and perfectly clear. They 
should be done wholly free hand, except perhaps large circles 
and long lines. 

Use blank paper (no cross-section paper) for sketching, 
don't draw to scale, but place all dimensions, measured from 
the machine, on the sketch. 

C — Laying Out Sheet and Lettering. 
Size of Drawing Board and Paper. — The size of drawing 
board has been suggested by the author as follows: All 
plates except those of Chap. VI on board 16 X 23 (or there- 



MECHANICAL DRAWING. 




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Visible Line of Solid 
In VI able Line o^^ohd 

Centre L/hf& 
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INTRODUCTORY REMARKS. 5 

about) with paper 13^ X 20. These plates have been care- 
fully laid out to suit this size of paper. 

For the plates of Chap. VI a somewhat larger board is 
recommended (20 X 26) with paper Y/y2 X 22, and all plates 
of Chap. W are laid out accordingly. 

Border Line (Fig. 2). — Draw border line one inch wide 
all around. Paper should not be trimmed. Never mind exact 
dimensions within border line ! 

Title (Fig. 3. — Every drawing, beginning with the first 
one, must have a title, consisting of Name of Object, Scale, 
Date, Plate No. and name of draftsman indicating year and 
course of study. 

Bill of Material (Fig. 4). — Each working drawing (not 
projection drawing) containing more than one part, must have 
a Bill of Material, stating name, material and number wanted 
of each item on the drawing. Each part may have its own 
sub-title, or it must be numbered to correspond with number 
on Bill of Material. In actual practice each casting must also 
have a pattern number. 

Laying Out Drawing. — In laying out a drawing it is advis- 
able to determine roughly the over-all dimensions of your 
drawing, so that it may be placed on the sheet with nearly 
equal margin all around. Always start from center lines. 
They not only make the start of any machine drawing easy, 
but they are also very important, as many dimensions are 
given from the center lines. For every part, that has a center, 
center lines must be shown, which also are to be inked in. 
When starting a plate first draw the principal axes of sym- 
metry and then build gradually around them. This also 
applies to rivets, bolts, shafts and all circular and cylindrical 
work. 



MECHANICAL DRAWING. 



— Gothic Leffers — 

A BCOErCH/JKLM 

NOPQR S TU VWX YZ 

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obcc/efgh/jk/mn 
opqrs tUvw^j^z 

- Block Lc/Aers - 

ABCDEFGHI 

JKLMNOPQ 

RSTUVW 



INTRODUCTORY REMARKS. 7 

After the drawing is completed in pencil, the drawing is 
either traced or inked in. 

Observe strictly the order of inking: Arcs, circles, straight 
lines, center lines, dimension lines, section lines, notes, title. 

Lettering. — The appearance of a drawing is greatly im- 
proved by good printing or lettering. Most text-books, how- 
ever, devote entirely too much space to this subject, showing 
all kinds and types of letters, difficult to execute and requiring 
a great deal of time, but which would not be tolerated in any 
drafting room, and may be of sole use to the sign painter. 
A good draftsman should make his letters free hand (unless 
ruled block-letters are required), and he should practice the 
two kinds most in use, ''Gothic Letters" and "Round Writing," 
see plate on. lettering. Gothic letters may be used either in 
capitals or small letters, or both combined. 

Round writing has the advantage of taking little time and 
affording a wide range of size of letters due to the different 
sizes of pens. Round writing always looks good and is very 
easily mastered. Practice with pen No. 2^ (don't forget clip 
over pen!), making the small letters yi", the capitals Y^" high. 

D — Important Rules as. to Working Drawings. 

The following rules should be studied very carefully. Th^y 
become of more importance after the first few plates, when 
they will be better understood. But from the very beginning- 
reference is made to these rules, and whenever this is done the 
student must study them and strictly adhere to them in his 
work. 

Rule 1. Conventional Lines. — Use only the following five 
lines (Fig. 5) : .. .. 

(a) Visible line of solid — heavy full line (or light and heavy 
in case of shading). 

(b) Invisible line of solid — medium, heavy broken line. 



8 MECHANICAL DRAWING. 

(c) Projecting lines — light broken line. 

(d) Center line — light dash and dot. 

(e) Dimension lines — light full line. 

Rule 2. Shade Lines. — They are not essential and not 
allowed on working drawings by most employers. They take 
up more time, but improve the appearance of the drawing. 
The light is assumed to come from the upper left hand corner 
at 45° in both plan and elevation (different from the rules of 
"Shades and Shadows"). Shading should be studied from 
the finished drawings in this book. Outlines of solids of revolu- 
tion (cylinder, rod, bolt, etc.) as a rule are not shaded. 

Rule 3. Scale. — Single machine parts are drawn to as large 
a scale as possible (full size preferably), depending, however, 
on space available. Use only the following scales : 

Full Size, Half Size, 3" = 1 ft. (K size), 1>4" = 1 ft. {ys 
size), 1" = 1 ft. (1/12 size), %" = 1 ft. (1/16 size), etc. 
(Found on the triangular boxwood scale.) 

Rule 4. Dimensions. 

(a) Every item represented on the drawing should be fully 
dimensioned. 

(b) The dimensions are those of the object, no matter what 
the scale may be. They are given in feet, inches and fractions 
of an inch. 

(c) Over 24" express in feet and inches. 

(d) Horizontal and vertical dimensions have the direction 
of their dimension lines and should be written as indicated on 
Plate 1. Note that fraction line coincides with dimension line. 
Note sharpness of arrows. 

(e) Dimension lines must not cross each other. 

(/) Show diameters (D. or dia.) in preference to radii (R. 
or rad.). 

(g) Never cross-hatch over dimensions. 



INTRODUCTORY REMARKS. 9 

Rule 5. Sections. 

(a) Working drawings are generally shown partly in sec- 
tion to show details of construction and form of casting, see 
Prob. 1, Plate 3. 

(b) Indicate kind of material by cross-hatching the areas 
as shown in Fig. 6. 

Fig. a. — Steel of all kinds. 
Fig. b. — Wrought iron. 

Fig. c. — Cast iron. When lines are drawn further apart, 
it may represent brick in section. 

Fig. d. — Brass and other similar copper alloys. 
Fig. e. — Babbitt, lead and similar soft metals. 
Fig. f. — Rubber, vulcanite and wood fiber. 
Fig. g. — In upper half : wood, when cut across the grain, 
in lower half : when cut along the grain. 

(c) Where different parts join in one view, the section 
lines are shown at right angles to each other. (See Cylinder 
in Fig. 7.) 

(d) All parts of the same piece must be sectioned in the 
same direction. 

(e) Sections that appear too thin, such as boiler plates, 
structural sections, etc., are often blackened in. In order to 
separate different pieces, a white line is usually left between 
them. Direction of light as in Rule 2. 

Rule 6. Finished Parts. — Finished parts are indicated by 
letter /. (See Plates 8 and 9.) If all is finished, state so by 
writing a note "finished all over." Some draftsmen prefer to 
draw a red line, where parts are to be finished. The "finishing" 
consists of machining the surface of the object, which accord- 
ing to the nature of the object may be accomplished by plan- 
ing, facing, turning, boring, or scraping. 
^ Rule 7. Cross-Sections. — Where in a sectional view the 



10 



MECHANICAL DRAWING. 



cutting plane passes through one of the following parts they 
should not be shown in section : Spokes, arms, ribs, bolts, 
rivets, valve stems, shafts, rods, etc. (Fig. 7.) 

Rule 8. Breaks. — Parts of considerable length are often 
shown broken. The break should indicate the shape of the 
object. Conventional methods of breaks are shown in Fig. 8, 



Nhee/ 




Fig. 7. 



Rule 9. Symmetrical Work. — In case of symmetrical work, 
mostly end views, consisting of a number of concentric circles, 
frequently only one-half of the view is shown. Fig. 9. 

Rule 10. Repeated Parts of Objects. — Where a flange is 
to be drilled for a large number of holes, only a few may be 



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F/af-- iron C/)anne/ 6c/r /fa// 



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Fig. 8. . 

shown, while the rest is indicated either by short radial lines 
or a note to that efifect. 

Similarly in a gear-wheel, where only two or three teeth 
need be shown and the total number be specified in a note 
(unless the instructor decides to have all teeth shown). Also, 



INTRODUCTORY REMARKS. 



11 



in riveted work only a few rivets may be shown, while the 
location of the rest is indicated by a suita'ble note. 

Rule 11. Abbreviations. — The following terms may be 
found on shop drawings : 



^ 



^ 




'^f>ool 



Hanc/ Whee/ 



Fig. 9. 



(a) 14 th'ds = 14 threads per inch (mostly referring to 
pipe threads.) 

{h) \" tap = hole to be tapped (threaded) to fit a \" bolt. 

(c) Drill = hole through object is drilled instead of cored 
(more accurate). 

(<i) Cored = hole through object is cored out (by pattern 
maker) and is not to be finished (drilled). 

(^) Fillet = this term applies to castings whose concave 
corners are rounded out (filled) to insure greater strength and 
smoother work in moulding. 



CHAPTER 11. 
SIMPLE V.'ORKING DRAWINGS. 
-- — r -cc -' :ciLs and Isometric. 
]^e:::2":cal : :_ is the art of nzaking- drawings enable of 
:t;:r -: : : g^ mechanical 5tr-.:::.:rr5 :.f .ole and in detail so 

clearly that skilled workmen ca:: :\ \ :t oiem without further in- 
formation, relying entirely on s :. :::r: :?.:"::. is r" rn on the 



BT-^^vmcf. 



0-ect IS re: 



L:ed in two or 



V dimen- 



z*- 10 a picture of a simple model 
:.i:e. B the top surface, and C the 




FiGL 10. Fia 11 

side surface If we look in the direction of the arr t :r :: 

surface A we obtain a front Tiew A : by looking at the top surrace 
B we obtain a top view (or plan) B, and by looking at the side 
surface C we obtain a side view C. These three view^ ire shown 



in Fig. 11. 



is show- 



front view A and the side 



view C to tiie right side of A. 



SIMPLE WORKING DRAWINGS. 



13 



Any surface of the object may be called the front view, pro- 
vided the other views are drawn in the proper relation to this 
view. Generally the principal and larger view is chosen as the 
front view. 

In working drawings these three views would not be suffi- 
cient unless they are fully dimensioned. See Prob. 1, Plate 1. 
This enables the mechanic to work from the drawing without 
taking refuge to scaling the drawing. 

Simple and particularly symmetrical models may be repre- 
sented in only front view and top view. Occasionally a very 
irregular object required special views in addition to the three 
views mentioned. For practice sake from the very beginning each 




Fig. 12. 



object should be represented in the three principal views men- 
tioned above. 

Isometric. — The "Isometric" of an object is a "one view" 
drawing of the three dimensions, height, breadth and thick- 
ness. "Isometric" means equal distances, that is, all lines, 
which are parallel, are drawn parallel contrary to a "Per- 
spective," where all lines converge. 

In practice a simple method to draw the Isometric is em- 
ployed. Taking as an example a prism. Fig. 12a, the edges 
of both faces are inclined at 30° to the horizontal. Further- 



14 



MECHANICAL DRAWING. 



more, all inclined lines are drawn full length, which, of course, 
never appears as such to the eye. 

Another more simple method, which should only be em- 
ployed when the object is too complicated, is the so-called 
Oblique Isometric, Fig. 12 h, c, d. 

Here one face of the object is represented as a correct front 
view and all lines in the front face are shown in their true 
lengths. Any angle may be assumed for the edges of the other 
faces. 

To approach somewhat real conditions, the following pro- 
portions are suggested : 

Edges drawn at 45° to horizontal — half of full dimension. 





Fig. 13. 

Edges drawn at 30° to horizontal — two-third of full di- 
mension. 

Edges drawn at 60° to horizontal — one-third of full di- 
mension. 

This rule applies also to the first method of drawing the 
Isometric. 



SIMPLE WORKING DRAWINGS. 15 

A third method, more difficult, but more accurate and more 
pleasing to the eye is by means of Projection. In Fig. 13 the 
Isometric is obtained by Projection from two views of a Pillow 
block. Both views are inclined in such a way as to have one 
face of the object become horizontal while the other face 
makes an angle of 30° with the horizontal. The angle of 16° 
45', which the base of the auxiliary view makes with the hori- 
zontal, has been found by computation. In Fig. 13^, the cylin- 
drical part K of the pillow block ought by projection appear as 
an ellipse in the Isometric. As this ellipse, however, is of 
nearly circular form, it is replaced by a circle by splitting the 
small difference a. 

B — Simple Models. 

On Plates A, B and C a number of models is shown in form 
of pictures, which in the absence of suitable models are to be 
used as problems for the first three drawing plates (optional 
with Instructor to expand work into more plates). 

Plate 1. Wooden Models. — Make a working drawing of 
three views of three solids assigned by Instructor from Plate A. 
Scale full size. Find suitable title for each model. Make list 
of material. Observe strictly rules 1, 2, 4d, 4e. 

Plate 2. Metal Models. — Make working drawing of three 
views and Isometric of two solids assigned by Instructor from 
Plate B. Scale full size. Find suitable title for each model. 
Choose kind of material. List of material. Observe same 
rules as in Plate 1. 

Plate 3. Machine Details. — Make working drawing of 
three views and Isometric of two solids assigned from Plate 
C. Scale 6" = 1 ft. Find suitable title for each model. Choose 
kind of material. List of material. Observe strictly rules 1, 
2, 4b, 4d, 4e, 4g, 5a, 5b. 



16 



MECHANICAL DR_\\VIXG. 



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SIMPLE WORKING DRAWINGS. 21 

C — Wooden Joints and Carpenter Work. 

On Plate D a number of points used in wood-working are 
shown, which, in the absence of suitable models, may serve as 
drawing problems for Plate 4 (also suitable for two plates). 

On Plates 5 and 6 wooden structures are shown, where such 
joints are employed. 

Plate 4. Wooden Joints. — Make working drawing of three 
views and Isometric of two wooden joints assigned by instructor 
from Plate D. Scale 6" = 1 ft. 

List of material. 

Plate 5. Frame Work. — Make working drawing of three 
views and Isometric (shown already on printed plate) of the 
frame-work. Scale %" ^=z \ ft. Make list of wooden joints em- 
ployed, and indicate same with letters in the frame-work. 

Plate 6. Drawing Table. — Make working drawing of three 
views and Isometric of drawing table. (Instructor may substitute 
other table or chest, etc., in drafting-room.) Scale 1^" = 1 ft. 
Copy drawing carefully from printed plate. 

D — Machine Drawings. 

The most important part of any machine is the machine bolt. 
Conventional ways of representing bolt threads are shown in 
Fig. 14. 

a. Double V thread. 
h. Single V thread. 

c. Single square thread. 

d. Single L. H. V thread. 

e. Double R. H. Sq. thread. 
/. V thread for small bolts. 

g. Any thread for very small bolts. 

There are a large number of special bolts in use. Be sure to 
remember the three most important ones : the "through bolt," 



MECHANICAL DR.\WIXG. 



PLftTE D. 




Brace Jwn/' 



SIMPLE WORKING DRAWINGS. 



23 



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MECHANICAL DRAWING. 



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SIMPLE WORKING DRAWINGS. 

''stud bolt" and "tap bolt," shown on Plate 7. Below is 
table of standard bolts and nuts. 



25 
given a 






£ 

^ 



6 



^ 



Fig. 14. 



Plate 7. Bolts and Nuts. 

(a) Correct way of representing threads: 

1. 3" V threaded screw and nut. 

2. 3" square threaded screw and nut. 







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26 



MECHANICAL DRAWING. 




SIMPLE WORKING DRAWINGS. 27 

(b) Conventional way of representing threads and nuts : 

1. ^ X 2%" through bolt. 

2. ^ X V/s" tap bolt. 

3. J/s X 3>4 stud bolt. 

4. 1" bolt nut. 
Scale, full size. 

Make a careful copy of printed plate 7. The unfinished parta 
of the drawing have to be completed. ^ 

Plates 8 and 9. — The author strongly recommends at this; 
point the use of larger machine models. Either of the following: 
ones may serve as good objects : Shaft Coupling, Shaft Hanger, 
Pillow Block, Pulley, Bench Vise. Where no models can be ob- 
tained, make drawings of Pillow Block and Seller's Shaft Coup- 
ling from Plates 8 and 9. In connection with these plates study 
carefully the following rules: At, As, 5a, 5b, 5c, 5<i, 6, 7, 8, 9, 11. 

Plate 10. Pipe Work. — Make Isometric as shown on 
printed plate and three views. Scale, 3" = 1 ft. Before attempt- 
ing this plate, make yourself thoroughly familiar with the various 
pipe fittings used here. Don't fail to get Manufacturers' Catalog! 



MECHANICAL DRAWING. 









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SIMPLE WORKING DRAWINGS. 



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CHAPTER III. 
PROJECTION DRAWING.* 

In Chap. II we have learned to represent objects by means 
of two or three views. When we are now called upon, not 
only to make a drawing of a solid, but also to clearly define 
its position in space, we take refuge in Projection Drawing, 
which treats Mechanical Drawing with mathematical accuracy. 

While it is evident that the art of Mechanical Drawing 
must have as its foundation an exact mathematical science, 
we must bear in mind that for the practical draftsman this 
science is of secondary importance and only serves the purpose 
of easier mastering the principles of Mechanical Drawing. 

Projection is the art of representing objects by views on 
two or three planes at right angles to each other in such a way 
that the forms and positions may be completely determined. 
These imaginary planes are called planes of projection, one be- 
ing horizontal, the others vertical. The walls and floor of a 
room may serve as an illustration. The position of a book, 
for instance, lying on a chair may be defined as follows : 30" 
above floor. 2 ft. away from rear wall, 3 ft. away from side wall. 

Method 1. — If we call the floor Plane 1, the rear wall Plane 
2, and the side wall Plane 3, we have Fig. 15a. If we now look 
at the solid in the direction of the arrows, as in Fig. 10, we 
observe the three views A, B and C on the three opposite 
planes. In ortographing projection we consider that all lines 
of sight producing the view are parallel to each other and per- 
pendicular (ortographic) to the planes. As it is impossible to 
show the three planes of projection at right angles to each 



*Xote — All problems dealt with in Tinsmith and Boiler work are 
based on problems in Projection Drawing. The developments are 
obtained in the same way, allowing proper lap for soldering, riveting, 
etc. 



PROJECTION DRAWING. 33 

Other on the flat surface of the drawing board, it is necessary 
to imagine P^ and P^ revolved until all three planes form one 
plane, Fig. 15b. 

By omitting the outer limiting lines of the planes we ob- 
tain the complete projection drawing of the solid, Fig. 15c. 

Method 2. — If we imagine walls and ceiling to be trans- 
parent, in other words, if the solid is enclosed within a glass 
box. Fig. 16a, we can trace the three views A, B and C of the 
solids on the outside of the three glass panes, as they appear 
to the eye, and if we, like in Method 1, revolve P^ and Pg until 
they form one plane with P^ we have Fig. 16b. The finished 
drawing appears in Fig. 16c. 

By comparing Method 2 with Method 1, we notice that in 
the second method the views appear arranged to each other in 
the same way as we have learned in Chap. I, Fig. 11. In 
many drafting rooms this method is preferred, that is, the top 
view is shown above instead of below the front view, and the 
right side view is shown, where it is seen, viz., to the right of 
the front view. The student should understand that any of 
these two methods may be used in mechanical drawing. Most 
of the following problems have been worked out on the first 
method, as this method seems to be better adapted to the 
study of Projection Drawing. 

In Figs. 15e and 16c the dotted lines are called projecting lines. 
The points of intersection of projecting lines with the planes of 
projection are the projections of the points. The lines of inter- 
secton of a plane with the planes of projection are the traces of 
the plane. 

iiti^ v A — Projections. 

Plate 11. Projection of Prisms. 

Prob. 1. Hexagonal prism, 1^" outside dia., 2^4" high. 

Prob. 2. Cube, \%" X 1^". 



34 



MECHANICAL DRAWING. 



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PROJECTION DRAWING. 35 

Prob. 3. Cylinder, 1^" dia., 2>4" high. 

Prob. 4. Irregular pentagonal prism, 2%'' high. 

Three Views and Development. — Where positions are not 
specified, arrange views to suit space available. Missing di- 
mensions, for instance, of base of Prob. 4 may be assumed. 

Developments. — The surface of a solid extended or spread 
out on a plane in its true size and shape is called the development 
of the surface. 

In ordej- to find the development of a prism one of its sides 
is supposed to be placed in contact with some plane, then the 
prism turned on the edge, until all faces have been placed on the 
same plane. Then add top and bottom. 

The development of a prism, then, consists of as many rect- 
angles joined together as the prism has sidesj-ih^se rectangles 
being the exact size of the faces of the prism, and in addition two 
polygons the exacts size of the bases. --' ^ " ^ 

Plate 12. Projection of Pyramids. 

Prob. 1. Cone. 

Prob. 2. Pentagonal pyramid. | 

Prob. 3. Hexagonal pyramid. ; i \ 

Prob. 4. Octagonal pyramid. ,_., . K ■ 

Three views and development. Circumserib^ng base circle 
1^" dia., height = 2>4". 

Developments. — A pyramid is developed by placing one 
of its sides on a plane surface, and rolling the pyramid on the 
plane, the vertex remaining stationary, until the same element 
is again in contact. The space rolled over will represent the; 
development of the surface qf the pyramids. All of the edges; 
of a regular pyramid are of the same length. 

From this it follows that the development of the surface of a 
cone, for instance, is mnde by describing the arc of a circle of \. 
radius equal to the length of an element, -,-„... _ J 



36 



MECHANICAL DRAWING. 





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PROJECTION DRAWING. 37 

Plate 13. Inclined Prisms. 

Prob. 1. Rectangular prism, 1%" X Vi" X l}i" high. 

Prob. 2. Hexagonal prism, 1%." base circle, 1J4" high. 

Prob. 3. Cylinder, V/s" dia., 1%'' high. 

Prob. 4. Irregular pentagonal prism, 1^" high. 

Pos. a. Perpendicular to Pj and parallel to Pg- 

Pos. b. Inclined at a = 60° to P-^ and parallel to P^. 

Pos. c. Inclined at a = 60° to P^ and /? = 30° to P^. 

Plate 14. Inclined Pyramids. 

Prob. 1. Quadralateral pyramid, 1^ x 1^ base, 2^" high. 

Prob. 2. Hexagonal pyramid, 1^" base circle, 2^" high. 

Prob. 3. Cone, l}i" base circle, 2^" high. 

Prob. 4. Pentagonal pyramid, 1%" base circle, 2%" high. 

Pos. a. Perpendicular to P^ and parallel to Pg. 

Pos. b. Inclined at a = 60° to P^ and parallel to Pg. 

Pos. c. Inclined at a = 60° to P^ and /? = 45° to P2. 

P — Sections. 

By "section" we understand any figure formed by the inter- 
section of a solid and a cutting plane. 

Plate 15. Sections of Prisms and Pyramids. 

Prob. 1. Right cone, 1%" base circle, 2^" high, cut by 
plane parallel P^ 1^" above base. 

Prob. 2. Irregular pentagonal pyramid, base within cir- 
cumscribing circle of 1%" diameter, 2^" high, cut by plane 
parallel P^ 1%" above base. 

Prob. 3. Hexagonal prism, face nearest Pg, making an 
angle of 15° with P^, l}i" outer diameter, cut by plane inclined 
to Pi at 45°, perpendicular to P^. Point of intersection with 
Pi = iy%" to left of axis of prism. 

Prob. 4. Cylinder, \y^" diameter, 2" high, cut by plane 
inclined to Pi at 45° and perpendicular to Pg. Point of inter- 
section with Pi, = l}i" to left of axis of cylinder. 



38 



MECHANICAL DRAWING. 








PROJECTION DRAWING. 



39 




40 



MECHANICAL DILWVIXG. 




PROJECTION DRAWING. 



41 




42 



MECHANICAL DRAWING. 



Three views and developments. 

When a regular solid is cut by a plane parallel to its base, 
as in Prob. 1 and 2, the section is a figure similar to the base. 

If the cutting plane is inclined to Fi, as in Probs. 3 and 4, 
the section will not be similar to nor of the same shape as the 
base, although it appears to the eye as such in the plan. The 
true sectional area, which would be perceived by looking at the 
section in the elevation at right angles, is found by revolving 
the cutting plane into a horizontal position and obtaining the 
points for the sectional area, where the projecting lines from 
the section and the plan view intersect. To find the develop- 
ment of the irregular pyramid in Prob. 2, find the true length 
of the edges, for instance, O — 1, by revolving the plan view, 
until such edge is parallel to P^- The new projection of the 
edge in elevation will show its true length. The development 
then is obtained by triangulation. 

Conic Sections. Sections cut by a plane from a cone are 
defined as conic sections. These sections may be either of the 
following (Fig. 17.) 

a. Circle. Plane parallel to base. 

h. Triangle. Plane passes through vertex. 

c. Ellipse. Plane inclined to base, cutting all elements. 

d. Parabola. Plane parallel to one element. 

e. Hyperbola. Plane parallel to axis. 

These sections appear as straight lines in elevation, while 
in plan they appear with exception of case b as curves. To 




Fig. 17. 



PROJECTION DRAWING. 43 

find points for these curves, we employ here for the first time 
the method of mixUia/ry cutting plcmes. Horizontal cutting 
planes passed through solids of revolution appear as circles in 
plan. And if the problem calls for the horizontal projection 
of a point shown in elevation on the surface of a solid of revo- 
lution, we pass an auxiliary cutting plane through this point 
and the intersection of this plane in Plan (as circle) with the 
vertical projecting line from the point in question will be his 
horizontal projection. 

Plate 16. Conic Sections I. 

Prob. 1. Triangular Section. Cutting plane passes 
through vertex and intersects P^ \" to left of axis. 

Prob. 2. Elliptical Section. Cutting plane inclined to P^ 
at 45"", intersects P^ 2" to left of axis. 

Cone 3" base, Zy," high. 

Three views and development. 

To obtain the plan in Prob. 2, we pass a number of auxil- 
iary planes, for instance, plane I which appears as circle I in 
plan and gives us two points a of the ellipse in plan. 

Another method for obtaining points for the curve consists 
of drawing a number of elements, for instance, "I," and find 
where they intersect the cutting plane. To this end the base 
circle may be conveniently divided into a number of equal 
parts. 

In order to find the development of the cone, Prob. 2, the 
true length of each element, for instance, 1 — a must be deter- 
mined. Its true length appears on the side element of the 
cone as 1^ — a^. 

The development of the top must be the true sectional area, 
which is found by the method given on Plate 15 Probs. 3 and 4. 



44 



MECHANICAL DRAWING. 




PROJECTION DRAWING. 



45 




46 



MECHANICAL DRAWING. 



Plate 17. Conic Sections II. 

Prob. 1. Parabolic Section. Cutting plane parallel to one 
element, intersects P^ 1" to left of axis. 

Prob. 2. Hyperbolic Section. Cutting plane parallel to 
and Ys" to left of axis. 

Cone 3" base, 3>^" high. 

Three views and development. 

To find curves of intersection, pass auxiliary cutting planes, 
for instance, I, which will furnish points a. 

The developments are found by dividing the base circle 
into any number of parts and determining the true length of 
each element. 

Spheric Sections. 

All spheric sections are circles and if the sections are paral- 
lel to P^ they appear as such in the plan. Therefore, to find 

the projection of a point located on 
the sphere, pass a cutting plane 
through the point, as shown in the 
elevation, and draw the horizontal 
projection of the cutting plane, which 
is a circle. In Fig. 18 a number of 
points given in one view are to be 
found in the other projection. For 
instance, find the horizontal projec- 
tion of point 2, having given its pro- 
jection, in the elevation. Draw cut- 
ting plane II parallel to the horizon- 
tal which will give circle II in the 
plan. The horizontal projection of 
^^^- ^S- point 2 is at the intersection of circle 

II and a line dropped from the vertical projection of point 2. 




PROJECTION DRAWING. 47 

Plate 18. Spheric Sections. 

Prob. 1. Cutting plane perpendicular to Pg and inclined 
at 45° to Pi, intersects P^ \}i" to left of axis. 

Prob. 2. Cutting plane perpendicular to P^ and inclined at 
45° to P^, intersects P^ 1^" to left of axis. 

Prob. 3._ Development of sphere, method 1. 

Prob. 4. Development of sphere, method 2. 

Diameter of sphere 2". 

In Probs. 1 and 2 the sections being inclined, the projection 
of the section is an ellipse, the points of which are found by 
means of horizontal cutting planes. The construction of the 
sectional area proves these apparently elliptical sections to be 
circles. 

Probs. 3 and 4 give two approximate developments of a 
sphere. In Prob. 3 the circumference is divided into a number 
of equal parts, which are joined by straight lines, thus trans- 
forming the circular section of the sphere into a polygon. 
Then these lines are produced until they intersect the center 
line and with these lines as radii the development of a cone is 
drawn, from which a development generated with the next 
smaller radius is deducted, leaving a narrow circular strip, 
representing the development of part of the sphere. This 
process is repeated for the rest of the sphere as indicated in 
the illustration. 

In Prob. 4 the sphere is cut like an orange into slices, and 
the surface of each slice is developed separately. The length 
of such a slice must equal half the circumference of the sphere. 
The curves of the strips are drawn by circular arcs, or, they 
may be constructed by finding their width at different points 
from the plan. 

Plate 19. Sections of Various Solids. 

Prob. 1. Machine nut for 4" bolt. 



48 



MECHANICAL DRAWING. 




PROJECTION DRAWING. 



4^" 



Prob. 2. Connecting rod stub ends. 

The solids represented here are or have been originally 
solids of revolution. A surface of revolution is generated by 
the revolution of a straight or curved line about an axis. 
Cones, cylinders, and spheres are examples of solids of revolu- 
tion. 

In Prob. 1 the machine nut was generated from a double 
(resp. single) cone, by passing through the cones six vertical 

and two (resp. one) hori- 
zontal cutting planes, Fig. 
19. The six vertical cut- 
ting planes are so placed 
as to form a regular hexa- 
gon when shown in plan 
and each of them, by its 
intersection with the sur- 
face of the cones, forms a 
curve which is an hyperbola. 
The elements of the cones 
form an angle of from 30° 
to 60° with the horizontal. 
To construct the curves 
pass a number of (equally) 
spaced horizontal cutting 
planes through the cones 
and vertical cutting planes. 
These will give a number 
of concentric circles in the plan of (regularly) varying 
diameters. The points of intersection of these circles with 
the sides of the hexagon, projected upon their respective cut- 
ting planes in the elevation, give points for the curves of the 
nut. 




Fig. 19. 



50 



MECHANICAL DILWVIXG. 




PROJECTION DRAWING. 



51 



Prob. 2 represents the stub end of a connecting rod, Fig.i 
20. It is cut from a solid of revolution, consisting of twoi 
superimposed cylinders of different diam-; 
eters joined by another solid of revolution,; 
by 4 vertical cutting planes v^hich fprm ai 
rectangular horizontal cross-section having; 
its center coincident v^ith that of the^ 
cylinders. The curve of intersection 
formed by the planes cutting the surface of 
revolution is found by means of cutting 
planes. 

Fig. 20. 




52 



MECHANICAL DRAWING. 















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PROJECTION DRAWING. 53 

INTERSECTIONS. 

C — Intersections. 

By "intersections" we mean the penetration of one solid into 
another. Where they meet we have the line of intersection, 
which must be geometrically located before we can make the 
developments. 

Plate 20. Intersection of Prisms I. 

Prob. 1. Horizontal prism 1% x l}i, 3" long. Faces in- 
clined at 45° to Pi and P^. 

Vertical prism Ij^ x 1^, 3" high, faces inclined at 45° to 

Prob. 2. Vertical prism 1^ x l}i, 3" high. Nearest edge 
to P2 yz" away from F^. Left face nearest Pg, making an angle 
of 60° with P2. 

Horizontal prism 1% x 1^, 3" long. Nearest edge to P2 
%" away from Pg. Lower face nearest P2, making an angle of 
30° with Pg. 

Three views and developments of vertical prisms. 

Plate 21. Intersections of Prisms II. 

Prob. 1. Vertical prism 1^ x 1^, 3" high. Nearest edge 
to P2 }i" away from Pg. Left face nearest P2 making an angle of 
30° with P2. 

Inclined prism 1^ x 1^, 3%'' long, parallel to Pg, making 
an angle of 20° with P^. Nearest edge to P2 5^" away from P2. 
Lower face nearest P2 making an angle of 60° with P2. 

Prob. 2. Horizontal irregular quadrilateral prism, 3" long. 
Vertical irregular pentagonal prism, 3" long. Assume rest of 
dimensfons. 

Three views and developments of vertical prisms. 

Plate 22. Locomotive Steam Boiler. 

Show correct developments of boiler sheet A-B-C, dome 
and slope sheet. 



54 



MECHANICAL DRAWING. 



















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PROJECTION DRAWING. 55 

First construct curve of intersection of dome and boiler by 
showing the elements of the dome in both views and project- 
ing the true length of the elements in the end view upon the 
front view. The development of the dome is thus easily found. 

In sheet A-B-C construct carefully the cut-out for the 
dome. Before developing the slope sheet, determine the sec- 
tional area of a plane passed at right angles to the sloping line, 
which will prove to be a semi-ellipse. The development of 
the slope sheet then consists of the development of an oblique 
prism of semi-elliptical cross-section, to which are added the 
two triangles a m n. 



56 



MECHANICAL DR-\WIXG. 





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PROJECTION DRAWING. 



57 



Plate 23. Intersections of Cylinders. 

Prob. 1.1 Flanged Y-branch. Main pipe 2y^" high, out- 
side diameter 2}4". Branch pipe 2^" long from intersection, 
outside dianeter \y^" . Angle between centres of pipes 60°. 
Offset of centres of pipes ^". Thickness of pipes Yz . 

Prob. 2. Inclined cross (half section). Outside diameter 
of pipes \y%" . Thickness of pipes = Yz' . Inclined cylinder 
makes an angle of 45° with P^ and an angle of 15° with P^. 

Show tiree views of each problem and developments as 
indicated oh plate. 

In Prob. 1 the axes of the two cylinders are on different 
but parallel planes. First draw the cylinders in elevation, 
neglecting the curve of intersection. Then determine the plan 
view, drawing auxiliary circles on the center line of the in- 
clined cylinder, by the use of which the horizontal projection 
of the flange may be obtained. The curve of intersection in 
the elevation is found from the plan. 

In Prob. 2 the inclined cylinder is shown inclined to both 
planes similar to position c of Prob. 3 on Plate 13. This is 
made possible by drawing an auxiliary projection, showing the 
inclined cylinder iil position h. 



58 



MECHANICAL DRAWING. 




PROJECTION DRAWING. S9 

Plate 24. Intersections of Spheres. 

Prob. 1. Sphere and Pentagonal Pyramid. Sphere 2y^" 
diameter. Dimensions of irregular pentagonal pyramid may 
be assumed. 

The problem of finding the curves of intersection is one of 
finding the intersections of a number of vertical cutting planes 
w^ith the surface of the sphere. These intersections are por- 
tions of circles, which appear as parts of ellipses, where the 
cutting planes are inclined to P^. 

Points of intersection in the elevation are found by passing 
through the solids a number of auxiliary planes parallel to P^- 

The circular cut-outs in the development of the prism corre- 
spond to the circles which are found by the intersection of the 
vertical planes of the prism and the surface of the sphere. 

Prob. 2. Sphere and cylinder. Hemisphere 3^" diam- 
eter, resting on P^. Cylinder 2" diameter. Axes of both 
solids on plane parallel Po? yk" apart. 

Determine the nature of the curve of intersection by the 
use of cutting planes. 

Prob. 3. Sphere and cone. 

Cone resting upon P^, height = 3>^", diameter of base = 
2y2\ Center 2y^' from P^. 

Diameter of sphere = 2^". 

Sphere to be placed within cone so that its surface is tan- 
gent to that of the cone. Plane passing through axes of 
sphere and cone to be perpendicular to P^, making an angle of 
45° with Pg. Show development of cone. 

There are 3 possibilities of intersection of a sphere and a 
cone, Fig. 21. 

a. Some of the elements of the cone do not intersect the 
surface of the sphere. 



60 



MECHANICAL DRAWING. 




PROJECTION DRAWING. 



61 



b. All of the elements of the cone intersect the surface of 
the sphere. > 

c. One element of the cone does not intersect the surface 
of the sphere. 





Fig. 21. 

Prob. 3 illustrates case c. The point of tangency T is 
found by an auxiliary projection, where the plane passing 
through the axes of both the cone and the sphere is parallel to P^ 
(see position b on plates 13 and 14.) 

Draw the required plan and elevation in the same way as the 
plan and elevation in position c is obtained from position b on 
plates 13 and 14, 

Points for the curves are found by means of cutting planes. 

Having developed the surface of the plain cone, points for 
the curves of intersection are found by laying off from the 
vertex of the development along each element, the distances 
from the vertex (obtained from the elevation) to the points of 
intersection of that element with the surface of the sphere. 



62 



MECHANICAL DR_\WING. 





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PROJECTION DRAWING. 63 

Prob. 4. Two Spheres. Their common axis inclined to 
both planes at 45° in projection. Diameter of spheres = 3>^" 
and 2^". Distance between centres in projection = 1^". 
Obtain limiting points of curves. Find true distance from 
M to M^ by a position b (see plates 13 and 14.) Curve of in- 
tersection to be found by means of auxiliary cutting planes. 

Plate 25. Intersection of Prisms with Pyramids. 

Prob. 1. Prism with pyramid. 

Irregular pentagonal pyramid 4}i" high, base in P^, vertex 
I^^'fromP,. 

Irregular horizontal pentagonal prism, 3^" long, base in- 
scribed in a circle 2}^" diameter; centre l}i" above P^ and IJ^" 
from Pf. Prism and pyramid to be constructed so that one 
edge of each solid remains unintersected. Draw the plan in each 
case (2 polygons) and obtain the two other views by projec- 
tion. To find the terminating points of the sides of the prism 
in plan, draw elements from the vertex of the pyramid 
through each of the edges of the prism, b, c, d, e, and show 
the horizontal projections of these elements intersecting the 
edges of the prism in the required points. Make development 
of both solids. 

Prob. 2. Cone with cylinder and sphere. 

Frustrum of cone, A" base diameter, 2^" top diameter, 2]/^" 
high, resting on F^, its centre 3^" away from P.^.- 

Semi-sphere ^Yz" diameter, centre on P^, ^". away from 
P^. Horizontal cylinder, \" diameter, inclined as 30° to Po? its 
axis Yz" above Pg. ^ 

Plate 26. Intersection of Cone with Oblique Prism. 

Height of cone 4i^", diameter of base 4" ; cone resti^ on P^ 
with centre line 3" from Pg. 

Base of oblique prism is an irregular pentagon, dimensions 
to be taken from plate. Projections of edges of prism on P., 



64 



MECHANICAL DRAWING. 




PROJECTION DRAWING. 65 

make an angle of 30° with P^. Projections of edges on P^ 
make an angle of 15° with Pg- (What is the true angle of 
inclination?) 

Points of the intersecting curves may be found by drawing 
horizontal cutting planes or by passing auxiliary planes 
through the vertex of the cone and an outside point S, which 
lies in P^ at its intersection with line OS parallel to the edges 
of the prism. 

Both methods may be employed in this problem and the 
results verified. 

Plate 27. Intersection of Cone with Pyramid. 

Cone 2>4" diameter, 6^'' high. 

Pyramid, 4^" high, base as per dimensions. 

This problem is solved in a similar way by the use of cut- 
ting planes which pass through the vertex of both pyramid and 
cone. 

D — Solids with Warped Surfaces. 

A warped surface cannot be developed by any of the methods 
previously referred to. It may be constructed approximately by 
the ''Method of Triangulation/' The construction is as follows : 
Lay off on the projections of the solid, small triangles at regular 
intervals, determine their true size and place them adjacent to 
each other. The base of each triangle is shown in the plan, the 
altitude in the elevation. Any warped surface may be developed 
in this manner. 

Plate 28. Development of Bath Tub. 

In constructing the development, we assume the tub being 
made in four pieces — A, A, B and C — the separating seams shown 
in plan at 1-2 and 0-9. 

The lower end of the tub forms part of a cone and should 
present no difficulty to develop. 

For the upper end the development will be obtained by 



66 



MECHANICAL DRAWING. 




PROJECTION DRAWING. 



GJ 




68 MECHANICAL DRAWING. 

triangulation. First obtain diagrams of triangles as follows : 
Divide both quarter circles at upper ends in plan into equal spaces 
and connect by lines 1-2, 2-3, etc. From the points 2, 4, 6 and 8 
drop lines to the elevation. 

Then the dotted lines in plan represent the bases of the tri- 
angles, whose altitudes are equal to the various heights in eleva- 
tion. For example, the true length of the line M in plan may 
now be taken from the line 6^-7 in the diagram of triangles. The 
development then consists of a number of triangles put together, 
the base of each being taken from the plan and the two sides 
taken from the dotted line of the Diagram of Triangles. 

The sides A are also developed by triangulation. 

First draw the Diagram of Triangles A. The horizontal 
lines 1-0 and 2-0, respectively, are equal to the corresponding 
lengths in plan. The vertical lines are equal to the lines 0-9 and 
e-o measured in elevation. The dotted diagonals are the true 
lengths of the lines 1-0 and 2-0, respectively. 



CHAPTER IV. 

PERSPECTIVE DRAWING. 

Perspective is the art of representing objects as they appear 
to the eye at a definite distance from the object. In orthographic 
(perpendicular) projection the views represent the object as 




Fig. 22. 

seen when the eye is iniinitely distant. By the perspective method 
then the Hnes drawn from points on the object to the eye converge 
and intersect at the point of sight. 

Before beginning the study of, perspective projection let us 
observe some of nature's phenomena of perspective. These 
phenomena become more apparent when we attempt to sketch 
from nature. We notice that the size of an object diminishes 



70 



MECHANICAL DRAWING. 



as the distance between the object and the eye increases. If 
several objects of the same size are situated at different distances 
from the eye, the nearest one appears to be the largest and the 




Fig. 23. 



others appear to be smaller as they are further and further away. 
At last the distance between the lines becomes zero and the 
lines appear to meet in a single point. This point is called the 
vanishing point of the lines. See Figs. 22, 23 and 24. By closer 
investigation of a drawing sketched from nature we find : 




Fig. 24. 



PERSPECTIVE DRAWING. 



74 



( 1 ) The limit of our visional observation is a horizontal line, 
situated at the height of our eye, called Horizon. 

(2) Objects of equal size appear smaller with increasing- 
distance. 

(3) Parallel lines converge into one point, called vanishing 
point. For horizontal lines this point is situated at the height of 
the eye, that is, it lies in the horizon, 

(4) Vertical lines appear vertical. 

(5) The location of the observer's eye is called the point of 
sight and is located in the horizon. 




When an object in space is being viewed rays of light, called 
visual rays, are reflected from all points of its visible surface to 
the eye of the observers. 

If a transparent plane, Fig. 25, be placed between the object 
and the eye the intersection of the visual rays will be a projection 
of the object upon the plane. Such projection is called the 
perspective projection of the object. The plane on which the 
projection is made is called the picture plane. The position of 
the observer's eye is the point of sight. 

This principle is illustrated by models where red strings 
represent the rays, piercing a glass plate. 



72 



MECHANICAL DRAWING. 



A — Perspective by Means of Plan and Elevation. 
Above can be put to practical use if we obtain a perspective 
projection in plan and elevation and then proceed by orthographic 
projection to obtain the perspective. 



^^^ 




Fig. 26. 



f^. /hint of I 



In Fig. 26 plan and elevation of a prism, such as is used on 
Plate 1, is shown, its front face making an angle with the picture 
plane. As a general rule, the object is placed behind the picture 



PERSPECTIVE DRAWING. 73 

plane with one of its principal vertical lines lying in the picture 
plane. P is the point of sight (the observer's eye). Its distance 
A from the picture plane in plan depends a great deal on the 
size of the object and it is important that the best view point is 
obtained. 

If a house about 40' high is to be sketched, the point of 
sight should be taken about 80' from the picture plane. A good 
rule to follow is to make this distance about twice the greatest 
dimension. When large objects are to be represented the best 
results are obtained when the point is taken nearly in front of 
the object. 

The distance of the horizon from the horizontal plane equals 
the height of the eye above ground and may be taken = 5' — 3. 
For high objects this distance may be increased and for low 
objects decreased. In our case it is shown slightly above the 
object. Pj is assumed on a vertical line half way between two 
lines dropped from the extreme edges of the diagram. This is 
not necessary, but it usually insures a more pleasing perspective 
projection. 

To obtain the perspective of any point of the object, for 
instance B, draw the visual ray in both plan and elevation to 
Pi and P2, respectively. From the point of intersection b in 
the picture plane (in plan and elevation) project perpendicu- 
larly and thus obtain the point B^, as perspective picture of the 
point B of the object. In this manner all the other points of 
the perspective are obtained. 

This method of construction requires no further explanation 
and may be applied wherever plan and elevation is obtainable. 

Plate. 29. Perspective of Cross. — Point of sight at a dis- 
tance Ht=2^" above floor and at a distance A=7j4" away from 
object, to be placed halfway between extreme points in plan. 



74 



MECHANICAL DRAWING. 




PERSPECTIVE DRAWING. 



75 



= B — Perspective by Means of Plan and Two Vanishing Points. 

Fig. 27 shows a rectangular prism in plan and elevation rest- 
ing upon a horizontal plane. 

The first step will be to redraw the plan, same as with the 
first method, behind the picture plane in plan, with the vertical 







Fig. 27.. 

line a-e lying in the picture plane and turned so that its long side 
makes an angle a (30°) with the picture plane. The point of 
sight (P2) is at a distance H above the floor and is located at 
the same height as the horizon. 

Next, find the vanishing points for the different systems of 
lines in the object. There are three systems of lines in the prism. 
Vab and Vad are found by drawing lines P^-B and Pi-D through 



76 



MECHANICAL DRAWING. 




PERSPECTIVE DRAWING. 11 

Pj parallel to a-b and a-d of the diagram and dropping vertical 
lines from the intersection of these lines with the picture plane 
(B and D) to the horizon, giving the vanishing points Vab and 
Vad. The third system of lines embraces the verticar lines which 
are drawn actually vertical and not converging towards one 
another. 

The edge a-e of the diagram, being in the picture plane, is 
called the line of measures, as it appears in its true size in the 
perspective view, and from a and e in the perspective view the 
lines will vanish at Vab and Vad, respectively, establishing by 
intersection with the vertical edges all points desired. 

Besides this principal line of measures other lines of measures 
may easily be established by extending any vertical plane in the 
object until it intersects the picture plane. This intersection, 
since it lies in the picture plane, will show in its true size and 
all points in it will show at their true height above the horizontal 
plane. 

If no line in the object should lie in the picture plane there 
would not be any principal line of measures, and some vertical 
plane in the prism must be extended until it intersects the picture 
plane. 

Instead of being some distance behind the picture plane the 
prism might have been wholly or partly in front of the picture 
plane. In any case, find the intersection with the picture plane 
of some vertical face of the prism. This intersection will show 
the true vertical height of the prism. 

Plate 30. Perspective of House.— Scale yi" — V. The 
projections are given. 

Long side of house making an angle of 30° with the picture 
plane. Nearest vertical edge of house to lie in the picture plane. 
Two perspective views of the house shall be obtained, the house 
being viewed from two different points. Their common distance 



78 



MECHANICAL DELWVING. 



in Plan A := 46'. The distances H^ and H, of the point of sight 
above the horizontal shall be 6' 6" and 31' 6", respectively. The 
construction of both views is exactly the same. 

The fact that the porch projects in part in front of the picture 
plane makes ::o dinerence in the construction of the perspective 
projecti'^n. 

C — Perspective by Means of Plan and One Vanishing Point. 

In this method the plan is placed with one of its principal 




Fig. 26. 



systems of korizontal lines parallel to the picture plane. This 
system tkerefore has no vanishing point, and as the vertical sys- 



PERSPECTIVE DRAWING. 



79 



tern has no vanishing point, only the third system of lines will 
have" a vanishing point. 

In Fig. 28 the vertical force of the prism lies in the picture 




Fig. 29. 



plane and shows in its true size. Its edges are lines of measures. 
The construction of the perspective is easily apparent from 
the illustration. 



80 



MECHANICAL DRAWING. 



Figs. 29 and 30 are problems of perspective solved by the last 
mentioned method. 



11 

id!.'::---!-. 




Fig. 30. 



CHAPTER V. 

SHADES AND SHADOWS. 

The problems of finding the shades and shadows of objects are 
problems dealing with points, lines, surfaces and solids, the same 
as are dealt with in orthographic projection. The employment 
of shades and shadows in drawings is an aid to a more realistic 
representation of the object illustrated and is chiefly found in 
connection with architects' work. 

Definitions : 

1. Shade. When a body is subjected to rays of light, that 
portion which is turned away from the light is said to be in shade. 

2. Shadow. When a surface is in light, and an object is 
placed between it and the light, that portion of the surface from 
which light is excluded is said to be in shadow. 

3. Umbra. That portion of space from which light is ex- 
cluded is called the umbra or invisible shadow. 

(a) The umbra of a point is a line. 

(b) The umbra of a line is a plane. 

(c) The umbra of a plane is a solid. 

(d) The shadow of an object upon another object is the inter- 
section of the umbra with the surface of the second object. For 
instance, shadow of sphere is an ellipse, rays being inclined to 
plane, umbra being a cylinder. 

4. Ray of light. The sun is the supposed source of light, and 
being at an infinite distance the rays of light are assumed to be 



82 



MECHANICAL DRAWING. 




SHADES AND SHADOWS. 



83 




Fig. 31. 



parallel. Although the direc- 
tion of the rays may be chosen 
arbitrarily, it has become cus- 
tomary to consider the rays as 
passing from the upper left 
over the left -shoulder of the 
observer upon the object and 
forming an angle of 45° with 
the horizontal line in both plan 
view and elevation. The true 
angle which the rays make 
with Pi = a = 35'' 15', which 
value has been found by 
computation. 

5. Shade line. The line of 

separation betwen the portion 

of an object in light and the portion in shade is called the 

shade line. It is made up of the points of tangency of rays of 

light tangent to the object. 

6. The shadow of the object is the space enclosed by the 
shadow of the shade line. In Fig. 31 the shade line of the given 
sphere is a great circle of the sphere. The shadow of this great 
circle on the given plane is an ellipse. The portion within the 
ellipse is the shadozu of the sphere. 

Plate 31. Points, Lines and Planes. 
Prob. 1. Point nearer P^. 
Prob. 2 and 3. Point nearer Pa- 

The shadow of a point falls always upon the plane, which is 
nearest to the point. In Prob. 3 the shadow of the point in plan 
is indicated aiid would be in a', provided the point were further 
removed from P,. a^-o', of course, must be horizontal. 



84 



MECHANICAL DILWVING. 




SHADES AND SHADOWS. 85 

Prob. 4, 5, 6 and 7. Shadows of lines. The Hnes purposely 
are shown with double lines, to bring out the construction. 

Prob. 4. Line _L P-^. Shadows indicated by heavy lines. 

Prob. 5. Line J_ P^. 

Prob. 6. Line II P^, inclined to P^. 

Prob. 7. Line II P^, inclined to P^. 

Determine shadow of two points of line (end points) and the 
connecting line is the shadow of the line. 

Prob. 8. Shadow of plane (triangle). 

Determine the shadow of the three corners 1, 2, 3 upon the 
planes of projection, then the triangles V-l'-Z' will be the 
shadows in plan and elevation, and only as much as appears on 
their respective plane will be visible and is shade-lined. The two 
shadows must intersect each other on the X-axis at a and h. 

Prob. 9. Shadow of circular plane. 

Plane is II to P^ and the distance so chosen, that the shadow 
of the circle falls completely upon P^. Choose any number of 
points on the circle (8) and find their shadow upon Fg- The 
points 1 to 8 will give us shadow V to 8', forming an ellipse. 

To determine the two axes of the ellipse cast the shadow of 
the circle upon P^, which is a circle O' of the same diameter as O. 
Draw circle O'" passing through centres O' and O" and draw 
mO" and nO" , cutting the ellipse in c and h. Then a-h is the 
major and c-d the minor axis of the ellipse. After the axes have 
been thus determined all other points of the ellipse may be found 
without the former method. 

Plate 32. Prisms and Pyramids. 

Prob. L Octagonal prism with octagonal flange. 

This object has its edges either vertical to or parallel to the 
co-ordinate planes and we can determine immediately the light 
and shade faces by applying to the object the projections of the 



80 



MECHANICAL DRAWING. 




SHADES AND SHADOWS. 87 

ray of light. These determine the shade lines. Then cast the 
shadows of ithese shade Hnes. 

Considering first the flange, it is evident that its top, left hand 
and front faces will receive the light, that the lower and right 
hand faces will be in shade. 

By casting the shadow of the flange, draw l-n at 45°, also the 
projection of the ray from L, which gives us the point o cor- 
responding to n. The ray from K terminates the shadow at Q. 

By producing plane d-e to r and drawing s-a, it is evident that 
the edge s-i-r casts its shadow upon the prism. The ray from 
R gives D. From here the shadow is horizontal to the ray from 
/ on 6^. Point U is found from the corresponding ray passing 
through c, point W from v-b. As a straight line is determined by 
two points lying in the line, it is evident that if we cast the shadow 
of the two ends of a line and draw straight lines between such 
points, such lines will be the required shadow. 

Prob. 2. Cylinder with square flatige. . ,: • 

By drawing c-b tangetit to fhe cylinder we obtain the shade 
line a in the elevation, b is the shadow on the wall. The shadow 
of the flange will be cast partly on the cylinder and on the wall. 
The shadow on the cylinder is part of a circle of the same radius 
as the cylinder. 

Prob. 3. Cylinder zvith round flange. 

Shade line a and shadows G are found as in Prob. 2 by draw- 
ing a G tangent to cylinder. To find points/ for the curve which 
is the shadow on cylinder and wall cast by the flange, any num- 
ber of rays are projected as indicated in the illustration. 

Prob. 4. Niche. 

The niche is half of a hollow cylinder topped by quarter of 
a hollow sphere. The shade for the cylindrical part is found by 
projecting rays a, b, etc., in both views. _, 

To find the shade for the spherical part, a number of cutting 



88 



MECHANICAL DRAWING. 




SHADES AND SHADOWS. • 89 

planes are passed through the soHd, perpendicular to P^. in the 
direction of the horizontal projection of the light rays. The inter- 
sections of these planes with the niche appear as curves in the 
elevation, for instance, D E H. The ray from D intersects this 
curve in D' and furnishes a point for the shade curve. 

Prob. 5. Cone. 

Part of the shadow falls on P^ and P^, according to the posi- 
tion of the cone on P^. By projecting the rays from the apex, 
point S'^ is found and by producing the ray in the plan we find 
S^ from which we draw tangents to the base of the cone, giving 
the shade lines a and h. 

Prob. 6. Cone standing on vertex. 

The shadow in the plan is found by first finding m^, which is 
the projection of the rays from m and M. M'^ being the center 
of a circle with radius equal to that of the base, draw tangents 
ma and mb and draw d^m and h'^m parallel to am^ and bm^. a^m 
and h'^m are the shade lines of the cone. 

To find the shadow in the elevation, which is part or the 
whole of an ellipse, according to the position in the plan, draw 
the projections of any number of rays as indicated in the illustra- 
tion. (See also Prob. 9, Plate 31.) 

Plate 33. Sphere and Ellipsoid. 

Prob. 1. Sphere. 

If we draw a cylinder tangent to the sphere in the direction 
of the rays of light, its diameter will be the same as the diameter 
of the sphere and its axis will pass through the center of the 
sphere. Each element will touch the sphere in one point and all 
these points lie on a plane perpendicular to the rays of light, and 
form a great circle of the sphere. The problem is simply that of 
finding the intersection of a cylinder with a plane. Upon h-h in 
the direction of the rays of light as a new horizontal, draw the 
sphere in the elevation and find the true angle of the rays of 



90 



MECHANICAL DRAWING. 




SHADES AND SHADOWS. 91 

light, which passes through W^ parallel to F-H. G^ and H^ are 
the points indicating the extreme shade lines of the circle and 
when projected upon circle m determine the major axis of the 
elliptical shade. 

The hemisphere G^ K^ H^ is in shade and the other hemisphere 
in light. At / is the greatest light, at G^ H^ is the greatest 
shadow, which can be best illustrated by dividing the sphere into 
a number of zones, and giving them a gradual shading. 

Prob. 2. Ellipsoid. 

In the elevation the ray is tangent in C and D, giving us E 
and F ; in the plan we obtain in the same way a h e f d c. 

To obtain further points for the shade lines we construct a 
number of cones tangent to the surface, for instance, / G, and we 
obtain by the same method as in Prob. 5 points g and G"\ 

Plate 34. Screw Surfaces. 

Prob. 1. Square threaded screw. 

Prob. 2. Square threaded nut. 

Prob. 3. V-threaded screw. 

These are rather difficult problems, as no further informa- 
tion is given. They need not be taken up in the regular course 
of study, although they form an excellent test of how far the 
student is enabled to solve problems without further aid, 
solely using his knowledge gained in previous work. 

Shadow Perspective. 

We distinguish here between a natural source of light (sun) 
and an artificial source (for instance, a candle). In the first case 
the rays of light enclose prisms, in the latter case pyramids. 

The laws of shades and shadows apply here too, for instance : 

The shadow of a point is there where its ray pierces the plane. 

Straight lines cast straight shadows upon planes. 

Parallel lines cast parallel shadows upon the same plane. 



92 



MECHANICAL DRAWING. 




SHADES AND SHADOWS. 



93 



The shadow of a straight Hne, which is parallel to a plane, cast 
upon the same plane is parallel to the line. 

If a straight line is perpendicular to a plane, its shadow takes 
the direction from the point where a vertical ray pierces the plane 
(foot point of ray of light). 

If we pass a plane through the light and the vertical line this 




Fig. 31-a. 

plane will intersect the horizontal plane in a straight line contain- 
ing the foot point of the ray. 

If the sun is the source of light the foot point for all horizontal 
planes lies perpendicular under the sun in the height of the eye. 

Plate 35. Shadow Perspective I. 

The perspective drawing of an interior and the source of light 
(candle) being given. 

Locate first the foot points 1, 2, 3 upon the various planes 
represented by walls, floors, ceiling, etc., and continue as outlined 
in the drawing. 



9i MECHANICAL DR.\\VIXG. 

In Fig. 31 -A the sun is the supposed source of light and located 
high above the picture plane. In this case all rays may be drawn 
parallel. 

Plate 36. Shadow Perspective II. 

Prob. 1. Point S below the horizon. 

The prism rests with its base upon P^. One face of the cube 
lies in the picture plane, thereby having only one vanishing point 
which is at F^. 

The point of sight is supposed to be opposite to H at the 
proper distance and a ray of light to pass through it, which 
pierces the picture plane in 5. Therefore 6^ is the vanishing point 
for the projection of all other rays. cS, dS, aS appear therefore 
as the projections of those which pass through a, c, d. Imagtae 
a plane passed through the vertical plane dd, and through the ray 
dS, we recognize SH as its trace and d^H as the line of inter- 
section with the horizontal plane. dS and d'^H being in the plane 
dd^SH, intersect in /. This is the shadow which d casts upon the 
horizontal plane. On the same plane lies d^I, which is the shadow 
oid^d. 

A vertical plane through cc^ and %-6' cuts the horizontal plane 
in the line c^H, upon which at 2 the shadow of c must lie. Like- 
wise a^H is the direction of the shadow of d^a and on this line the 
point 3 is the shadow of a. 1-2 is shadow of dc, but as this line is 
horizontal, both must be parallel and have J' ah as .vanishing point. 
Line l-o as shadow of c-a must also be parallel and vanish toward 
the same point Vhd. 

The construction of the shadow of the cube is shown in the 
drawing, yn-n is a vertical line, with n upon the horizontal plane. 
tyi-n may represent the height of the human figure standing at 
n. no is direction and length of its shadow cast on the horizontal 
plane. 



SHADES AND SHADOWS 



95 




Fig. 31-b. 



If the vanishing point vS' for all rays of light lies below the 
horizon it indicates that the sun is behind the observer and that 
the fronts of all objects are in light. 

If, on the other hand, 6^ were above the horizon the light 



96 MECHANICAL DR.\WIXG. 

would come from behind and the front of all objects would be 
in shade. 

Prob. 2. Point S aboz'e the horizon. 

Construction of shades and shadows may be understood from 
drawing. 

-\nother problem worked out on this principle is shown in 
Fie. 31-B. 



CHAPTER VI. 
ADVANCED MECHANICAL DRAWING. 

A — Working Drawings. 

The problems on the next five plates, 37, 38, 39, 40 and 41, are 
good examples of assembly drawings. In the absence of suitable 
models they may serve as drawing plates. Steam engine and 
generator should be worked out in form of a complete set of 
detail drawings, each detail being represented in as large a scale 
as possible (preferably full size). From his own detail drawings 
the student then should work out the different views of the engines 
complete. And here, again, the author wishes to emphasize the 
great importance of making intelligible freehand sketches of the 
various machine parts from the given assembly drawings or, still 
better, from actual machines. These sketches are to be entered 
in a special notebook kept for the purpose. The student should 
also record in this book any new rule for proportioning machines, 
tables, formulas and standards of machine drawing, relating to 
bolts, castings, pattern, machine shop work, etc., always stating 
the source of his information in each case for future reference. 

At this stage of our work the student should take up the 
study of elementary machine design and strength of materials, 
and in connection with his drawings should peruse good text 
books on machine design, steam engines, etc., as collateral read- 
ing. Only the most important facts in connection with the draw- 
ing plates are touched upon here so as to stay within the scope 
of this book. 

Plate 37. 2" Globe Valve. 

Make working drawing of every detail in two views, scale 
full size, also assembly either full or half size, depending on 
space available. Only over-all dimensions to be inserted in as- 
sembly. Complete list of material : A Body, B Bonnet, C Disk 



98 



MECHANICAL DILWVIXG. 




I 



ADVANCED MECHANICAL DRAWING. 99 

Holder, D Lock Nut, E Disk Nut, F Valve Disk, G Spindle, H 
Gland Nut, / Follower, / Hand Wheel. (Don't fail to get manu- 
facturer's catalog!) 

Plate 38. Marine Steam Engine. 

Description: The steam engine converts heat into mechanical 
work. 

Its working is briefly as follows : A piston is moved in a 
cylinder by the pressure of steam alternately in opposite direc- 
tions. This reciprocating motion is converted into rotary motion 
through the connecting rod and crank. A slide valve in the 
steam chests admits steam alternately to both ends of the cylinder 
through the steam ports at either end. 

When the valve is in the position shown steam enters the 
upper end of the cylinder and drives the piston downwards. At 
the same time the lower end is connected with the exhaust pipe, 
through which the steam escapes into the atmosphere (or into 
a condenser in case of a condensing engine). 

The slide valve is moved by an eccentric which acts like a 
small crank. It is set in such a way that steam is shut off to 
either end of the cylinder before the piston has completed its 
stroke (point of cut-off). The motion of the piston is continued 
during the remainder of the stroke by the expansive force of 
the steam. 

As this particular type of engine is a marine engine it must 
be able to reverse its motion. This is accomplished by a peculiar 
arrangement of two eccentrics operated by a combination of 
levers, which is called the "Stevenson Link Motion." The ends 
of the eccentric rods are connected by a link on which slides a 
block to which the valve rod is connected. By shifting the link 
either eccentric rod can be brought opposite the slide block and 
then the valve receives motion from that eccentric {full speed 
forward or full speed reverse). In any intermediate position of 



100 



MECHANICAL DRAWING. 




ADVANCED MECHANICAL DRAWING. 101 

the slide block it gets a motion due to both eccentrics, travel of 
the valve is reduced and cut-oif occurs earlier. Result : Engine 
slows down. Exactly at the centre the motion of the valve is too 
small to admit steam effectively. Result : Engine stops. 

Make full set of working drawings of each detail. 

Redraw assembly with only over-all dimensions inserted. 

Plates 39, 40, 41. D. C. Generator. 

Description: A generator (dynamo) converts mechanical 
energy into the energy of currents of electricity. 

It consists of three essential parts : 

(a) The field magnet to produce a powerful magnetic field. 

(b) The armature, a system of conductors wound on an iron 
core and revolving in the magnetic field in such a manner that 
the magnetic flux through these conductors varies continuously. 

(c) The commutator, by means of which the machine is con- 
nected to the external circuit. 

Specifications: 165 k. w., 550-500 volt, 300 amp., 400 rev. per 
minute. 

Eight poles with 1,700 windings of 1.8 mm. wire. 

Armature of 98 cm. diameter, length of iron 32 cm., height 
of iron less height of teeth 16.6 cm. 

Number of conductors on periphery 500, measuring 2.4 x 
12 cm. 

Number of grooves 250, measuring 3.4 cm. deep by 0.5 
cm. wide. . 

Commutator of 60 cm. diameter, length 20 cm., 250 segments. 

Make full set of working drawings to decimal or inch scale. 

B — Elementary Designing and Construction. 

(a) Riveted Joints and Structural Work. 

A riveted joint is, unlike a bolted joint, a permanent fastening. 
The plates of such a joint overlap and have one or more rows oi 



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MECHANICAL DR_\WING. 






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RIVETED JOINTS, 103 

rivets, arranged either zig-zag or opposite each other. The plates 
may butt against each other and have either single or double 
w^elt strips. - 

Rivets and Rivet Holes. — Usually the rivet is 1/16 in. less 
in diameter than the hole. All holes should be drilled after the 
plates have been bent or flanged and put together in their proper 
places. 

Symbols. — d = dia. of rivet, t = thickness of plates, t ^ 
thickness of w^elt strip, p = pitch, 1 = lap. 
In each case / = l>4<i. 
Plate 42. Riveted Joints. 

Prob. 1 to 5. Common forms of rivet heads: (1) Button, 
(2) and (3) Steeple, (4) Conical, (5) Countersunk. 

d=l" t=9-16". Scale, full size. 
Prob. 6. Single riveted lap joint. 

d=t+^ p=2d+/4) foi* iron plates and iron rivets. 

d^t-|-7-16 p=2d-|-^, for steel plates and steel rivets. 
Prob. 7. Double riveted lap joint (zig-zag). 

d=t+5-16 p=:3d-|-/4j foi" ^^on plates and iron rivets. 

d=t+% p=:3d-|-^, for steel plates and steel rivets. 
Prob. 8. Single riveted butt joint with double v^elt strips. 

d=t4-/4 P=3d-f-%, for iron plates and iron rivets. 

d=t+5-16 p=3d-j-^, for steel plates and steel rivets. 
Prob. 9. Double riveted butt joint v^ith double v^elt strips. 

d=t-|-^ p^3d-|-l, for iron plates and iron rivets. 

d=t+5-16 p=3d-|-%, for steel plates and steel rivets. 
Prob. 10. Double riveted lap joint (chain spacing). 

d=t-|-5-16 p=:3d+/4, for iron plates and iron rivets. 

d=:t+% p=3d-[-^, for steel plates and steel rivets. 
Prob. 11. Treble riveted lap joints. 

d=t-}-5-16 p=3d-f J^, for iron plates and iron rivets. 

d=t+^ p=3d-}->4, for steel plates and steel rivets. 



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MECHANICAL DRAWING. 




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RIVETED JOINTS. 105 

Prob. 12. Double riveted butt joint with double welt strips. 
d=:t+^ p=i2d4-/4» for iron plates and iron rivets. 
d=t+3-16 p^2d+^, for steel plates and steel rivets. 

The pitch in each case has been calculated so as to make the 
shearing strength of the rivet equal the tensile strength of the 
plates, ti = ys t. 

Distance between adjacent rivets, measured from centre to 
centre of rivet, whether in the same or different rows, should not 
be less than 2d, from which determine value of c. Assume dif- 
ferent values for d in each case. Use steel plates and steel rivets. 
Scale 6" = V. 

Plate 43. TwoFlue Boiler. 

Make complete working drawing as outlined. Each sheet for 
boiler, flues and dome to be fully and accurately dimensioned. 
List of material. Scale to suit paper. 

Structural Drafting. 

Structural drafting is generally subjected to the same require- 
ments as mechanical drawings. A few special characteristics 
may be mentioned, however. 

Shade lines are seldom used; they are apt to destroy the ac- 
curacy of the diagram in scaling. Also, the simplest form of let- 
tering is adopted, owing to the fact that numerous notes are 
necessary. 

Structural frames are made of rolled forms, designated by the 
forms of their sections. The shapes commonly used are plates 
and bars of square, round, flat, angle, channel and Z sections and 
I beams. Catalogues issued by the different mills, give dimen- 
sions and principal properties of these sections besides much other 
valuable information, and should be in the hands of every struc- 
tural draftsman. 

Besides those abbreviations mentioned in connection with 
mechanical drawing there are several abbreviations typical of 



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CAMS. 107 

structural drawing. For instances, rolled shapes are designated 
by their form of section : 2^ x 2^ x ^ L, etc. PL stands for 
Plate, Sp. PI. for sphce plate, Fig. PI. for flange plates, etc. 

Plate 44. Roof Truss. 

Scale y^" == 1 ft. Follow all instructions stated on plate. 
{h) CAMS. 

A cam is a plate or cylinder having a curved outline or a 
curved groove in it, which by its rotation about a fixed axis im- 
parts a backward and forward motion to a piece in contact with it. 

The motion which cams are designed to give to their followers 
may be Uniform motion or varying motion. 

Uniform Motion. 

If a body moves through equal spaces in equal intervals of 
time, it is said to have uniform motion ; that is, its velocity is 
constant. 

Varying Motion. 

If the mechanism which moves the piece is so designed as to 
start and stop gradually, the shock will be avoided. The char- 
acter of the motion usually employed in this case is either what 
is known as (a) harmonic motion or (b) uniformly accelerated 
and retarded motion, also called gravity motion. 

(a) Harmonic Motion. If a point A travels around the 
circumference of a circle with uniform velocity, and another 
point B travels across the diameter at the same time at such a 
velocity that it is always at the point where a perpendicular let 
fall from A would meet the diameter, the point B would be said 
to have harmonic motion. Its velocity will increase from the 
starting point until it reaches the centre and from there its veloc- 
ity gradually decreases to zero at the end of the path. 

(b) Gravity Motion^A^v uniformly accelerated and retarded 
motion, is also" a| motion where the velocity gradually increases 
until if reaches a maximum at the middle of the path, and from 



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CAMS. 



109 



there gradually decreases to the end. The rate of increase and 
decrease, however, is different from that in harmonic motion, the 
velocity being increased in gravity motion, by equal amount in 
equal intervals of time, the spaces traveled over in successive in- 
tervals of time being in the ratio of 1, 3, 5, 7, etc., to the middle 
of the path and decreasing in the same ratio to the end. 

Kinds of Cams. 

Cams may be divided into two general classes, plate cams and 
cylindrical cams. Either one of these may be designed for uni- 




FiG. 32. 

form motion, for harmonic motion, for gravity motion, or for a 
combination of two or even of all three. 

The action of a cam will be most easily understood by the 
study of an example. In Fig. 32 a rotating cam is to be designed 
to give its follower a reciprocating motion along a straight line 



110 



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CAMS. Ill 

passing through the cam centre, the velocity being uniform 
throughout both strokes if the cam rotates with uniform angular 
velocity. 

Since the cam rotates uniformly, while the follower moves 
with uniform velocity, the cam describes equal angles while the 
follower traverses equal distances. Divide the throw into any 
convenient number of equal parts, say six, and divide the half- 
revolutions of the cam into the same number of equal angles. 
The curve drawn through the points of intersection will be an 
Archimedean spiral and the same kind of curve will be found for 
the remaining half of the cam. 

In practice the end of the follower is provided with a roller, 
for the sake of lessening friction, such as is used with the cams 
on plates 45 and 46 and the real outline of the cam itself will then 
not be the curve shown in Fig. 32, but a line drawn tangent to a 
series of circles whose centers lie on the curve shown, and whose 
diameters are all equal to that of the roller on the follower. 
(Prob. 1, Plate 45.) 

A cam frequently has to actuate a point on a lever, which 
moves in the arc of a circle. The construction of the cam is the 
same as above, but the throw is now measured and divided along 
a circular path instead of along a straight line. (Prob. 4 and 5, 
Plate 45.) 

In Prob. 3, Plate 46, the line of motion of the follower point 
does not pass through the centre of rotation of the cam. If the 
lengths of the tangents measured from centre of roller to point 
of tangency is equal to the corresponding arcs, the curve of cen- 
tres would be an involute. Such curves are generally used for 
the cams of ore-crushing stamp mills. 

The motion of the follower may be expressed graphically by 
means of a "Diagram of Motion," which is a Displacement Dia- 
gram on a time base, the abscissae (horizontal distances) meas- 



112 



MECHANICAL DRAWING. 




CAMS. 113 

uring time (expressed in angles to any scale) and the ordinates 
(vertical distances) measuring displacement of follower (any- 
suitable scale), 

Plate 45. Cams I. 

Proh. 1. Uniform Motion Cam (straight-line motion). 
Throw = I", Roll = %" dia., Hub = iy%" dia, 

Proh. 2. Uniform Motion Cam. Throw = Y^", Roll = 
^" dia., Hub =1^" dia. Three throws during each revolution. 

Proh. 3. Positive Action Cam (uniform motion). Motion 
as per diagram. Plate dia. = S", Roll ^ %" dia., Hub = \}i" 
dia. 

Proh. 4. Uniform Motion Cam (swinging motion). Throw 
(measured on arc) = I", Roll = ^" dia., Hub = 1^" dia. 
Length of lever = 2>^". . , 

Proh. 5. Uniform Motion Cam (swinging motion). Mo- 
tion as per diagram. Roll = }i" dia., Hub = 1^^" dia. Length 
of lever = 2". 

Scale full size. 

Plate 46. Cams 11. 

Proh. 1. Harmonic Motion Cam. Throw = 1^", Roll = 
%" dia.. Hub = iy2" dia. 

Proh. 2. Positive Action Cam (harmonic motion). Throw 
= l}i", Rolls = \%" dia.. Hub = \y2" dia. - i 

Proh. 3. Knock-off Cam. Throw = 2", Roll = I" dia.. 
Hub = iy2" dia. 

Proh. 4. Cylindrical Cam. Throw during half revolution 
= Ys", rest during second half revolution. Roll =1" dia. 

Scale 6"= 1 ft. " i 

C — Tooth Gearing. 

When two shafts are far apart motion from one shaft to 
another is transmitted by belting running over suitable pulleys. 
When the shafts are close together, motion is transmitted by 



114 



MECHANICAL DRAWING. 




Fig. 33. 



TOOTH GEARING. 115 

tooth-gearing. Different gear may be employed, depending on 
the relative position of the shafts. The following three princi- 
pal cases may arise : 

(a) Shafts parallel to each other. (Spur-wheels.) 

(b) Shafts perpendicular to each other, lying in the same 
plane. (Bevel wheels.) 

(c) Shafts perpendicular to each other, lying in different 
planes. (Worm and wheel.) 

Construction of Curves for Tooth Profile. — In order that 
two wheels geared together have a uniform velocity ratio, the 
forms of teeth must be such, that the common normal at the point 
of contact always passes through the pitch point, which divides 
the line of centres in the inverse ratio of the angular velocities. 
The curves, whose normals are easily found, are the Involute 
and Cycloid. 

(a) Involute. By unwinding a string wrapped about a 
cylinder the end describes the Involute. Lay off tangents at 
regular intervals and make their length equal to the arc meas- 
ured from the point of origin to the point of tangency. 

(b) Cycloid. A point on the circumference of a circle 
called the rolling circle rolling on a straight base describes a 
Cycloid. If the rolling circle rolls upon a circle as base we have 
the Epicycloid, and if the rolling circle rolls within a circle as base, 
we have the hypocycloid. Should the diameter of the rolling circle 
= the radius of the base circle, the hypocycloid will be a straight 
line. In the following plate the construction of the curves is 
sufficiently illustrated. 

Plate 47. Involute and Cycloids. 

Make drawing on small size of drawing paper and work out 
all problems shown on printed plate. Where the involute is to 
pass through a given point reverse construction, that is, lay off 



116 



MECHANICAL DRAWING. 




TOOTH GEARING. 117 

tangent passing through the point upon the arc and find point 
of origin. 

Construction of Tooth Profile. 

A. Involute. — Two-spur wheels are assumed to be tan- 
gent to each other with their pitch-circles in the pitch-point. 
Through the pitch-point pass the line of action, which experience 
has found to give the best proportions when drawn at an angle of 
15° to the horizontal. Tangent to this line of action draw the 
two base-circles. 

Upon these two base-circles construct the involute, arrang- 
ing it so that both curves pass through the pitch-point. The 
points of origin therefore lie to the right and the left re- 
spectively of the pitch-point. 

Draw the addendum and dedendum. 

Next lay off the thickness of the tooth (half the circular 
pitch). The involute curve forming the addendum of the tooth 
extends below the pitch line to the base line. The balance of 
the flank of the tooth is drawn radial, joining the rim with a 
small fillet, whose radius is equal to the clearance. 

In case of a rack or a worm meshing with an involute wheel, 
the face and flank of the teeth form one straight line, which is 
normal, that is perpendicular to the line of action. Fig. 33-B. 

B. Cycloid. — (Fig. 33-A.) The curve of the face of the 
tooth is an epicycloid and of the flank a hypocycloid. The 
diameter of the rolling circle should not be greater than the 
radius of its pitch circle (otherwise tooth will be too weak at the 
root) and not smaller than half the radius. Where the diam- 
eter of the rolling circle equals the radius of the pitch circle, the 
hypocycloid will be a straight line passing through the centre 
of the pitch circle and the flank of the tooth will be radial 
( "Radial flank system'' ) . 



118 



MECHANICAL DRAWING. 




TOOTH GEARING. 119. 

For interchangeable wheels the same rolling circle must be 
taken, in any other case the same rolling circles may be taken 
for both wheels or their diameters may be taken in proportion 
to their respective pitch circles. 

Proportions of Iron teeth: 

TT D 

Circular pitch p = , D = pitch diameter, n = number 

n 
of teeth. 

D 

Diametral pitch p^ ^ — 
n 

Addendum of tooth 1 = .3 p. 

Dedendum of tooth 1^ = .4 p. 

Thickness of tooth t = .5 p for cut teeth, = .48 p for C. I. 
teeth. 

Plate 48. Tooth Gearing I. — Involute System. 

Prob. 1. Worm and wheel, scale 6" = V. 

Prob. 2. Spur wheel and pinion, scale 3" = V. 

Show detail construction of teeth full size. 

Plate 49. Tooth Gearing II.-— Cycloidal System. 

Bevel wheel and pinion. Scale 6" ^ V. Show all teeth in 
projection in the various views. Detail construction of teeth. 
(d) Valve Motion Diagram. 

Valve diagrams show the relative movements of the valve 
and the piston and the various events occurring during one 
stroke. Numerous forms of diagrams are used, the most con- 
venient one being Zeuner's diagram. 

(1) Zeuner*s Diagram. — In Fig. 34 the diameter of the large 
circle represents the displacement of the slide valve. When 
the valve is in position OP, the vertical projection OM repre- 
sents its displacement from centre position. Make OQ := OM. 
If this construction is repeated, we obtain a pair of circles, 



120 



MECHANICAL DRAWING. 




VALVE MOTION DIAGRAM. 



121 



which is the polar displacement diagram of the valve. For 
instance, if OR is the position of the eccentric, then the corre- 
sponding displacement from centre position is OS. 

To find the position of the crank L of the engine for a given 
position OP of the eccentric, make angle POL = 90° + 5. 




Fig. 34. 



Fig. 35. 



Or, if OQ is marked off on OL instead of on OP (Fig. 35), it 
will be found that the locus of Q is a pair of circles on the 
centre line OE, the angle COE being equal to the angle of 
advance. 

Plate 50 shows the complete valve diagram. The obliquity 
of the connecting rod has not been taken into account. 

The crank pin circle may be drawn to any convenient size. 
It is shown here to coincide with the displacement circle of the 
valve. 

OA — Position of crank for beginning of admission. 

OB — Position of crank for beginning of stroke. 

OC — Position of crank for beginning of expansion. 

OD — Position of crank for beginning of exhaust. 

OE — Position of crank for beginning of compression. 

Below this diagram is shown the probable form of the 
indicator diagram. The construction of the expansion and com- 



122 



MECHANICAL DRAWING. 



pression (isothermal or hyperbolic) curves is illustrated in Fig. 
36. In actual practice the steam line usually slopes down- 



Pl/' Constant 




Fig. Ze. 



wards a little because of the falling pressure due to the de- 
creasing port opening. 

(2) The Valve Ellipse is a great assistance in understand- 
ing Zeuner's valve diagram, and it also shows the speed with 
which the valve moves at different parts of its stroke, when 
opening or closing the ports. 

The diameter of the crank circle may be divided into 10 
equal parts and the chords of the valve circle (polar diagram) 
laid oft' as ordinates for the valve ellipse (linear diagram on 
displacement base.) For instance, at the dead point the port 
is open to the extent of v. 

Reuleaux's Diagram. — The diagram constructed by Pro- 
fessor Reuleaux is also very convenient for the solution of simple 
valve problems. 

Mark off on a line making an angle 5 with the vertical, the 
outside lap e, inside lap i, and steam port a. 

Starting from the dead-point when the crank has moved an 



VALVE MOTION DIAGRAM. 123 

angle a to the position oh, the valve has moved a distance hi 
from its central position. The port-opening is hj. 

The lead is found by drawing a perpendicular from B upon 
AC, as this is the port-opening when a ^= O. 

The maximum port-opening is a. 

Cut-off takes place at C. Steam admitted at A. 

Plate 50. Valve Motion Diagram. 

Make a valve motion lay-out by means of Zeuner's and Reul- 
eaux's Valve diagram for a single slide valve steam engine. 
Also construct the valve ellipse. The dimensions of slide valve 
and ports are to be taken from the marine engine plate. Angle 
of advance = 35°. Scale of diagram three times full size. 

Draw up probable indicator diagram for 65 lbs. abs. pressure 
and 17.5 lbs. back pressure. Scale of pressures I" = 20 lbs. As- 
sume 10 per cent, clearance volume. 

Show the valve and piston in the positions A, B, C, D, E. 

Also show the valve in centre position, fully dimensioned. 

In these positions the valve is to be shown full size, while the 
engine mechanism may be shown to any convenient scale. 



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